Captain America's Shield is basically a Greater Artifact. (I don't know what kind of terms they have for it in 4e/5e, but it's definitely an Artifact, probably a Greater Artifact in 3e terms).
It's unique, it cannot be reproduced (in the Marvel Cinematic Universe it's because SHIELD doesn't have enough vibranium to make a second one, in the main Earth 616 comic continuity it's because they couldn't replicate the freak accident that lead to its forging), it's virtually indestructible. The only time I can think of it being broken was during Secret Wars, when the power of the Beyonder could break, but not annihilate, it. . .and it basically took the equivalent of a Wish to restore it, there's probably another example, but it takes a cosmic being, of godlike power (far beyond Thor and the Asgardians) to break it, in D&D terms basically an Overpower. It's an item of legend: In the Captain America movie when the excavation team saw the shield in the ice, they instantly knew what it was and what it meant.
That's not just any shield, and is definitely not something for a 1st level character. That's pretty much an Artifact by any normal D&D definition of the term.
Want to play Captain America as a Paladin? That's great. He is a pretty ideal example of the Paladin mindset, and I've seen him used before as a model of how to play a Paladin. However, I'd start with the roleplaying first. Even Cap started World War II with a mundane shield before he got his signature item.